I'm not sure I understand your case. However, I stated that there are cases where it is worse than O(N^2). The runtime is highly dependent on the contents of the matrix. In many cases it takes fewer than N^2 iterations. Occasionally it takes more. On average it seems to be roughly O(N^2), but again that depends a lot on what is in the matrix. I got that result by trying different ways of filling the matrix. I tried things like randomly setting each pixel with various probabilities, placing random horizontal and vertical segments, placing random squares, or placing random filled squares. I did all of those both in black on white and white on black. In all of those cases, going from n=1000 to n=2000 resulted in a runtime increase of less than a factor of 4.
Don On Jan 23, 10:33 pm, bharat b <[email protected]> wrote: > @Don: the solution is very nice.. But, how can u prove that it is O(n^2).. > for me it seems to be O(n^3) .. > > Ex: nxn matrix .. all 1s from (n/2,0) to (n/2,n/2). > all 1s from (n/2,0) to (n,0). > > > > > > > > On Thu, Jan 17, 2013 at 9:28 PM, Don <[email protected]> wrote: > > The downside is that it uses a bunch of extra space. > > The upside is that it is pretty fast. It only does the time-consuming > > task of scanning the matrix for contiguous pixels once, it only > > searches for squares larger than what it has already found, and it > > doesn't look in places where such squares could not be. In practice it > > performs at O(n^2) or better for most inputs I tried. But if you are > > devious you can come up with an input which takes longer. > > Don > > > On Jan 17, 10:14 am, marti <[email protected]> wrote: > > > awesome solution Don . Thanks. > > > > On Thursday, January 17, 2013 12:38:35 AM UTC+5:30, marti wrote: > > > > > Imagine there is a square matrix with n x n cells. Each cell is either > > > > filled with a black pixel or a white pixel. Design an algorithm to > > find the > > > > maximum subsquare such that all four borders are filled with black > > pixels; > > > > optimize the algorithm as much as possible > > > -- --
